Precision Distances to Dwarf Galaxies and Globular Clusters from Pan-STARRS1 3π RR Lyrae

In this paper, we exploit the opportunities provided by the Pan-STARRS1 (PS1) 3π RR Lyrae catalog (Sesar et al. 2017) to explore the Galactic halo. Using that large data set of RRab stars covering three quarters of the sky out to more than 130 kpc, in Hernitschek et al. (2018) we looked at the seemingly smooth part of the stellar halo. We now focus on the RRab stars in globular clusters (GC) and dwarf galaxies in order to determine their distances and constrain their structure. For most of these objects, RRab stars may be the most precise distance tracers. As shown in Section 8, all GC and dwarf galaxies we study here are beyond any parallax precision of Gaia DR2, which is according to Bailer-Jones et al. (2018) only valid within a heliocentric distance range of about 5 kpc. The main advantages of such a study are that due to the large angular extent and depth of PS1 3π, the source of observational data as well as the methodology are the same for all GC and dwarf spheroidal (dSph) galaxies we analyze. The aim of this paper is to precisely constrain the position and extent of each of these overdensities from RRab stars, where we determine these properties for 29 GC and 11 dSph galaxies, and if this is not possible, to at least give their mean heliocentric distances. Furthermore, from the globular clusters we demonstrate that the period–luminosity relations used by Sesar et al. (2017) to determine the distances of the RRab stars are precise and their predicted magnitudes are well within the claimed uncertainties.

RR Lyrae stars (RRL) as distance indicators have the advantage of being low-mass stars found in both early- and late-type stellar systems (van den Bergh 1999). When periods, or periods and metallicities, for RRL are known, their distances can be estimated using period–luminosity (PL) or period–luminosity–metallicity (PLZ) relations. Visual magnitude–metallicity relations are described for example in Chaboyer et al. (1996), Bono et al. (2003), and Cacciari & Clementini (2003). In the infrared, the extinction is smaller and the amplitude of variation is smaller. In the near-infrared (NIR), well-defined PL relations can be found (Longmore et al. 1986; Bono et al. 2001, 2003; Catelan et al. 2004; Braga et al. 2015; Sesar et al. 2017), extending to the midinfrared with only small scatter (Madore et al. 2013; Klein et al. 2014).

These individual distance estimates can then be used to calculate distances to and the shape of globular clusters as well as dwarf galaxies. Dwarf galaxies orbiting our Milky Way are not only interesting objects per se, but can also provide us with important information to determine the Milky Way's total mass and dynamics. Dambis et al. (2013) used WISE as well as zero-points from HST parallaxes to derive PL relations from 360 RRL belonging to 15 globular clusters.

More recent work on the distances of globular clusters was carried out by Neeley et al. (2015) who investigated mid-IR PLZ relations for the globular cluster NGC 6121 (M4), which is not in our sample because it lies outside of the PS1 3π footprint. Their work contains PL relations for both the RRab and RRc samples as well as for the combined RRab+RRc sample. In their 2017 paper, Neeley et al. (2017) also present theoretical mid-IR PLZ relations for RR Lyrae stars at Spitzer and WISE wavelengths and show that the mid-IR PLZ relations can provide distance estimates to individual RR Lyrae stars with uncertainties better than 2%. This is comparable to the result by Sesar et al. (2017) derived for the RRab stars with optical photometry used in this paper. For the dSph Sculptor, which lies outside of the PS1 3π footprint, Garofalo et al. (2018) derived mid-IR PLZ relations and calculated the distance to the dwarf galaxy as part of the Spitzer SHMASH project, which targeted in total four dSph (Ursa Minor dSph, Bootes dSph, Sculptor dSph, and Carina dSph).

This paper is structured as follows. In Section 2, we introduce the PS1 3π survey and lay out the properties of the PS1 RRab stars. This is followed in Section 3 by a description of the spatial area covered by PS1 3π, and the list of GCs and dSph that are included in it. In Section 4, we present the method of fitting a series of parameterized stellar density models and the probabilistic approach to constrain their model parameters. We describe fitting tests on mock data in Section 4.3. In Section 5, the position and extent are estimated for each GC and dSph. We present various analyses based on these fitted parameters. In Section 6, we calculate mean distances for those dwarf galaxies and GC, which do not have enough sources for the fitting process. We also discuss the implications on PL relations in Section 7 and compare our distance estimates to those derived using the second Gaia data release in Section 8. A discussion and summary of our results is given in Section 9. The main part of the paper is followed by a large Appendix containing figures as well as tables.

As in our previous papers, e.g., Hernitschek et al. (2017) and Hernitschek et al. (2018), our analysis is based on a sample of highly likely RRab stars, as selected by Sesar et al. (2017) from the Pan-STARRS1 3π survey. Here, we briefly describe the pertinent properties of the PS1 3π survey and the RR Lyrae light curves obtained, and recapitulate briefly the process of selecting the likely RRab for the catalog of PS1 RRab stars, as laid out in Sesar et al. (2017). We also briefly characterize the obtained candidate sample.

The Pan-STARRS 1 (PS1) survey (Kaiser et al. 2010) collected multi-epoch, multicolor observations undertaking a number of surveys, among which the PS1 3π survey (Chambers et al. 2016) is currently the largest. It has observed the entire sky north of decl. −30° in five filter bands (g_P1, r_P1, i_P1, z_P1, y_P1) with a 5σ single epoch depth of about 22.0, 22.0, 21.9, 21.0, and 19.8 mag in g_P1, r_P1, i_P1, z_P1, and y_P1, respectively (Stubbs et al. 2010; Tonry et al. 2012).

Starting with a sample of more than 1.1 × 10⁹ PS1 3π sources, Hernitschek et al. (2016) and Sesar et al. (2017) subsequently selected a sample of 44,403 likely RRab stars, of which ∼17,500 are at R_gc ≥ 20 kpc, by applying machine-learning techniques based on light-curve characteristics. RRab stars are the most common type of RR Lyrae, making up ∼91% of all observed RR Lyrae (Smith 2004), and displaying the steep rises in brightness typical of RR Lyrae.

The identification of the RRab stars is highly effective, and the sample of RRab stars is pure (90%) and complete (≥80% at 80 kpc) at high galactic latitudes. Distances to these stars were calculated based on flux-averaged i_P1 magnitudes, corrected for dust extinction using extinction coefficients of Schlafly & Finkbeiner (2011) and the dust map of Schlafly et al. (2014). The distance estimates are precise to 3%, based on newly derived PL relations for the optical/near-infrared PS1 bands (Sesar et al. 2017). Overall, this results in the widest (three quarters of the sky) and deepest (reaching >120 kpc) sample of RR Lyrae stars to date, allowing us to observe them globally across the Milky Way. Out of these sources, 1093 exist beyond a Galactocentric distance of 80 kpc, with 238 beyond 100 kpc, which enables us to estimate distances to and extents of dwarf galaxies and globular clusters. RRc stars, which were also selected by Sesar et al. (2017), are not included in our study.

PS1 3π, as it covers the entire sky north of decl. −30° out to more than 130 kpc, gives us access to many globular clusters (GC) and several dwarf galaxies.

To select those overdensities for which fitting their density might be feasible, we started with a list of dwarf galaxies within 3 Mpc by McConnachie (2012), its update from 2014⁷ and a list of currently known globular clusters from the 2010 update of Harris (1996). We excluded the ones outside the PS1 3π footprint and made plots of regions on the sky around for each of the remaining ones. If an overdensity is apparent in the PS1 RRab sample from visual inspection, we consider it for further analysis. We ended up with a list of 11 dwarf galaxies and 29 globular clusters within PS1 3π, as given in Tables 1 and 2. Plots of a subset of these overdensities are found in the Appendix, Figures 1–11. For plotting those overdensities, we chose a Cartesian projection of (l, b) to more easily compare to their marginalized distributions in l and b (histograms). With this choice, high-latitude overdensities such as NGC 5024, NGC 5053, and NGC 5272 appear to be elongated in the l direction.

We expected that the central regions of the globular clusters might not be well represented due to crowding and blending effects that made many RRab stars fail to meet the criteria for inclusion in the catalog of PS1 RRab stars (Sesar et al. 2017). To test that, we compared our sample with the Catalog of Variable Stars in Globular Clusters from Clement et al. (2001). There are 11 globular clusters detectable with RRab stars both in the catalog of PS1 RRab stars and the Catalog of Variable Stars in Globular Clusters. As shown in Figure 12, we find that for each of the 11 globular clusters available in both catalogs, our catalog misses most RRab in the globular cluster's central regions. The dSph galaxies are sufficiently diffuse that this is not a significant issue.

In this section, we lay out a forward-modeling approach to describe the spatial distribution of RRab stars within and near overdensities such as dwarf galaxies and globular clusters. We are using a local halo model describing the background of field stars from the halo as in Hernitschek et al. (2018) and a smooth spheroidal distribution describing the overdensity itself. Regarding the dwarf galaxies, this approach is similar to Martin et al. (2008), who derived structural parameters of Milky Way satellites from SDSS data.

We presume that the local stellar halo distribution can be sensibly approximated by a spheroidal distribution with a parameterized radial profile (see also Hernitschek et al. 2018). The overdensities can be described by multivariate Gaussians in (l, b, D). Following a number of previous studies (e.g., Sesar et al. 2013; Cohen et al. 2015; Xue et al. 2015; Iorio et al. 2017; Hernitschek et al. 2018), we presume that the overall radial density profile of the halo outside of overdensities—the distance-dependent "background" of field stars in a given direction—can be described by a power-law profile. We attempt to carry out the fit on small 5 × 5 deg² patches on the sky around the assumed position prior (l_prior, b_prior). We thus neglect the selection effects and halo flattening described in Hernitschek et al. (2018) and instead fit for a local stellar halo distribution as a function of a power-law index n only.

We apply a forward-modeling process to fit stellar-density models to the data by generating the expected observed distribution of stars in the RRab sample, based on our model for the halo background and overdensity. The predicted distribution is then automatically compared to the observed star counts to calculate the likelihood.

4.1. Stellar Density Model

For the overall radial density profile of the halo stars, we assume a power-law model

$$\begin{eqnarray}&&{\rho }_{\mathrm{halo}}(X,Y,Z)={\rho }_{\odot \mathrm{RRL}}{\left({R}_{\odot }/{r}_{q}\right)}^{n},\end{eqnarray} \tag{ 1 }$$

where ρ_⊙RRL gives the number density of RR Lyrae at the position of the Sun, n is the power-law index where larger values of n indicate a steeper profile, R_⊙ is the distance of the Sun from the Galactic center, and ${r}_{q}=\sqrt{({X}^{2}+{Y}^{2}+{(Z/q)}^{2})}$ is the flattening-corrected radius.

In Hernitschek et al. (2018), we derived the halo flattening on concentric ellipsoids. However, as we deal here with very small patches on the sky, and do not want to derive a reliable fit for the halo but want to remove any background distribution, we decided to set q = 0.75, leaving n the only free parameter for the halo component. Also, we are not fitting for ρ_⊙RRL.

The spatial density of an overdensity, i.e., a dwarf galaxy or globular cluster, is described by a multivariate Gaussian ${ \mathcal G }$:

$$\begin{eqnarray}&&\begin{array}{l}{\rho }_{* }(l,b,D)={ \mathcal G }(l,b,D)\\ \quad =\ \displaystyle \frac{\exp \left(-0.5\left[{\left(\tfrac{l-\bar{l}}{{\sigma }_{l}}\right)}^{2}+{\left(\tfrac{b-\bar{b}}{{\sigma }_{b}}\right)}^{2}+{\left(\tfrac{D-\bar{D}}{{\sigma }_{D}}\right)}^{2}\right]\right)}{{\sigma }_{l}{\sigma }_{b}{\sigma }_{D}{\left(2\pi \right)}^{(3/2)}}.\end{array}\end{eqnarray} \tag{ 2 }$$

The data set ${ \mathcal D }$ is given as ${ \mathcal D }=(D,\delta D,l,b)$. The parameters are ${\boldsymbol{\theta }}=(\bar{l},\bar{b},\bar{D},{\sigma }_{l},{\sigma }_{b},{\sigma }_{D},{f}_{* },n)$, composed of the spatial position of the overdensity $(\bar{l},\bar{b},\bar{D})$, its extent (σ_l, σ_b, σ_D), and the fraction of the stars f_* in the overdensity, and the power-law index n of the halo model. The heliocentric distance distribution of stars is then characterized by

$$\begin{eqnarray}\begin{array}{rcl}{p}_{\mathrm{RRL}}({ \mathcal D }| {\boldsymbol{\theta }}) & = & {p}_{\mathrm{halo}}({ \mathcal D }| {\boldsymbol{\theta }})+{p}_{* }({ \mathcal D }| {\boldsymbol{\theta }})\\ & = & \ (1-{f}_{* })\times {\hat{\rho }}_{\mathrm{halo}}(l,b,D,n)\\ & & +\ {f}_{* }\times {\hat{\rho }}_{* }(l,b,D,\bar{l},\bar{b},\bar{D},{\sigma }_{l},{\sigma }_{b},{\sigma }_{D}),\end{array}\end{eqnarray} \tag{ 3 }$$

where

$$\begin{eqnarray}&&{\hat{\rho }}_{\mathrm{halo}}(l,b,D,q,n)\equiv \displaystyle \frac{{\rho }_{\mathrm{halo}}(l,b,D,q,n)}{\int {\rho }_{\mathrm{halo}}(l,b,D,q,n){dD}},\end{eqnarray} \tag{ 4 }$$

with an analogous definition of ${\hat{\rho }}_{* }$.

Although we were aware of a distance uncertainty of 3% for RRab stars from Sesar et al. (2017), we have not included it in our calculations yet. The reason for this is that the distance uncertainty can easily be taken into account later on, as the distance uncertainty _D ∼ 0.03D adds in quadrature to the (true) width in distance:

$$\begin{eqnarray}&&{\sigma }_{D}=\sqrt{{\left({\sigma }_{D}^{^{\prime} }\right)}^{2}+{\epsilon }_{D}^{2}}.\end{eqnarray} \tag{ 5 }$$

We will deal with the distance precision versus true line-of-sight depth later when we evaluate our fitting results.

4.2. Constraining Model Parameters

With the model ${\rho }_{\mathrm{RRL}}({ \mathcal D }| {\boldsymbol{\theta }})$ at hand, we can directly calculate the likelihood of the data ${ \mathcal D }$ given the model ρ_RRL and the fitting parameters ${\boldsymbol{\theta }}$.

The normalized unmarginalized logarithmic likelihood for the ith star with the observables ${{ \mathcal D }}_{i}$ is then

$$\begin{eqnarray}&&\mathrm{ln}p({{ \mathcal D }}_{i}| {\boldsymbol{\theta }})=\displaystyle \frac{{\rho }_{\mathrm{RRL}}({{ \mathcal D }}_{i}| {\boldsymbol{\theta }})| {\boldsymbol{J}}| }{\int \int \int {\rho }_{\mathrm{RRL}}(l,b,D| {\boldsymbol{\theta }})| {\boldsymbol{J}}| {dldbdD}},\end{eqnarray} \tag{ 6 }$$

where the normalization integral is over the observed volume. The Jacobian term $| {\boldsymbol{J}}| ={D}^{2}\cos b$ reflects the transformation from (X, Y, Z) to (l, b, D) coordinates.

We evaluate the logarithmic posterior probability of the parameters ${\boldsymbol{\theta }}$ of the halo model, given the full data ${ \mathcal D }$ and a prior $p({\boldsymbol{\theta }})$, $\mathrm{ln}p({\boldsymbol{\theta }}| { \mathcal D })=\mathrm{ln}p({ \mathcal D }| {\boldsymbol{\theta }})+\mathrm{ln}p({\boldsymbol{\theta }})$ with

$$\begin{eqnarray}&&\mathrm{ln}p({ \mathcal D }| {\boldsymbol{\theta }})=\displaystyle \sum _{i}\mathrm{ln}p({{ \mathcal D }}_{i}| {\boldsymbol{\theta }})\end{eqnarray} \tag{ 7 }$$

being the marginal log likelihood for the full data set.

To determine the best-fit parameters and their uncertainties, we sample the posterior probability over the parameter space with Goodman & Weare's Affine Invariant Markov Chain Monte Carlo (Goodman & Weare 2010), making use of the Python module emcee (Foreman-Mackey et al. 2013).

The final best-fit values of the model parameters have been estimated using the median of the posterior distributions; the uncertainties have been estimated using the 15.87th and 84.13th percentiles. For a parameter whose pdf can be well-described by a Gaussian distribution, the difference between the 15.87th and 84.13th percentile is equal to 1σ.

Our model has eight free parameters, ${\boldsymbol{\theta }}=(\bar{l},\bar{b},\bar{D},{\sigma }_{l},{\sigma }_{b},{\sigma }_{D},{f}_{* },n)$, and each star has three-dimensional coordinates (l, b, D). As we attempt to carry out the fit on small 5 × 5 deg² patches on the sky around the assumed position prior (l_prior, b_prior), we always have a sufficient number of overdensity and background RRab stars for the fit as shown in Figures 1–11. The overdensity itself is fit by a three-dimensional Gaussian describing the spatial position of the overdensity $(\bar{l},\bar{b},\bar{D})$ and its extent (σ_l, σ_b, σ_D). Thus a minimum number of two RRab stars within the overdensity, in addition to the background, is needed for a successful fit, albeit with large uncertainties when the number of RRab is small. All overdensities for which we later claim fitted positions and spatial extents meet these criteria, i.e., the minimum number of RRab stars is 3.

4.2.1. Model Priors

We now lay out the "pertinent range," across which the priors for the model parameters ${\boldsymbol{\theta }}=(\bar{l},\bar{b},\bar{D},{\sigma }_{l},{\sigma }_{b},{\sigma }_{D},{f}_{* },n)$ are given. Based on Tables 1 and 2, we can set priors on $\bar{l}$, $\bar{b}$, $\bar{D}$. In general, we allow a rather wide prior, i.e., allow the on-sky positions to vary around the object's center by ±5°, and the heliocentric mean distance $\bar{D}$ to vary by ±20 kpc. In cases with a second overdensity nearby (i.e., NGC 5024, NGC 5053), we set more rigid priors on $\bar{l}$, $\bar{b}$, $\bar{D}$. As the halo profile tends to vary a lot on such small patches on the sky as are evaluated here, we allow the power-law index n to vary between 1.7 and 5.

Our complete prior function is then:

$$\begin{eqnarray}\begin{array}{rcl}\mathrm{ln}p({\boldsymbol{\theta }}) & = & \mathrm{Uniform}(0.05\leqslant {f}_{* }\lt 1)\\ & & +\ \mathrm{Uniform}(1.7\leqslant n\lt 5.0)\\ & & +\ \mathrm{Uniform}(\mathrm{log}| \bar{l}-{l}_{\mathrm{tab}}| \lt \mathrm{log}{\mathtt{offset}}\_{\mathtt{\deg }})\\ & & +\ \mathrm{Uniform}(\mathrm{log}| \bar{b}-{b}_{\mathrm{tab}}| \lt \mathrm{log}{\mathtt{offset}}\_{\mathtt{\deg }})\\ & & +\ \mathrm{Uniform}(\mathrm{log}| \bar{D}-{D}_{\mathrm{tab}}| \lt \mathrm{log}{\mathtt{offset}}\_{\mathtt{kpc}})\\ & & +\ \mathrm{Uniform}(\mathrm{log}(0.1)\lt \mathrm{log}({\sigma }_{l})\lt \mathrm{log}(10))\\ & & +\ \mathrm{Uniform}(\mathrm{log}(0.1)\lt \mathrm{log}({\sigma }_{b})\lt \mathrm{log}(10))\\ & & +\ \mathrm{Uniform}(\mathrm{log}(0.1)\lt \mathrm{log}({\sigma }_{D})\lt \mathrm{log}(20)),\end{array}\end{eqnarray} \tag{ 8 }$$

where the index "tab" denotes the values from Tables 1 and 2, respectively, and offset_deg = 5°, offset_kpc = 20 kpc for all overdensities except for NGC 5024, NGC 5053. For NGC 5024 and NGC 5053, we set the offset to offset_deg = 1°.

4.3. Fitting Tests on Mock Data

When trying to fit all dSph from Table 1 and globular clusters from Table 2, we found that the data available for some of them do not allow for a reasonable fit. For the Crater II dSph at a distance of ∼120 kpc, the PS1 RRab catalog does not contain enough sources for a good fit, not surprising given the large distance. As Sagittarius dSph lies at the edge of the PS1 3π footprint, we cannot successfully fit its on-sky position (l, b), but we can fit its heliocentric distance D. Among the globular clusters, we have to exclude NGC 4147, NGC 5634, NGC 5694, NGC 5897, IC 1257, NGC 6093 (M80), NGC 6171 (M107), NGC 6356, NGC 6402 (M14), NGC 6426, NGC 7099 (M30), Pal 1, and Pal 13, as in those cases, we find too few, if any, RRab stars associated with these overdensities picked up by the PS1 3π survey.

In Tables 3 and 4 as well as in Figures 1–11, we give the dSph and GC best-fit parameters we get from successfully carrying out the fitting as described in Section 4. Tables 3 and 4 list the name, fitted position (l, b, D), fitted angular extent σ_l, σ_b, and depth σ_D assuming a multivariate Gaussian, as well as the derived linear extents (Δl, Δb, ΔD) as

$$\begin{eqnarray}&&{\rm{\Delta }}l=2\sqrt{2({\left(D\cos (b)\right)}^{2})(1-\cos ({\sigma }_{l}))}\end{eqnarray} \tag{ 9 }$$

$$\begin{eqnarray}&&{\rm{\Delta }}b=2D\tan ({\sigma }_{b})\end{eqnarray} \tag{ 10 }$$

$$\begin{eqnarray}&&{\rm{\Delta }}D=2{\sigma }_{D}.\end{eqnarray} \tag{ 11 }$$

Table 3.  Fitted Dwarf Galaxies

Name	Fitted	Fitted	Δl [kpc]	Δb [kpc]	ΔD [kpc]	ΔD/Δl	ΔD/Δb	Sources
	(l [°], b [°], D [kpc])	(σl [°], σb [°], σD [kpc])
Draco dSph	${86.37}_{-0.01}^{+0.01}$, ${34.71}_{-0.01}^{+0.01}$, ${74.26}_{-0.18}^{+0.18}$	${0.13}_{-0.01}^{+0.01}$, ${0.13}_{-0.01}^{+0.01}$, ${2.40}_{-0.15}^{+0.17}$	0.28	0.33	4.81	14.48	14.66	191
Sagittarius dSph	—, —, ${28.18}_{-0.10}^{+0.10}$	—, —, ${1.01}_{-0.01}^{+0.02}$	2.02	—	—	—	—	538
Sextans dSph	${243.55}_{-0.04}^{+0.04}$, ${42.26}_{-0.03}^{+0.04}$, ${81.42}_{-0.40}^{+0.41}$	${0.26}_{-0.03}^{+0.03}$, ${0.23}_{-0.03}^{+0.04}$, ${3.24}_{-0.37}^{+0.43}$	0.55	0.66	6.49	9.83	9.87	99
Ursa Major I dSph	${159.38}_{-1.48}^{+2.07}$, ${54.43}_{-0.39}^{+2.79}$, ${94.33}_{-4.94}^{+10.80}$	${0.34}_{-0.20}^{+2.53}$, ${0.33}_{-0.19}^{+2.05}$, ${2.59}_{-1.11}^{+5.90}$	0.65	1.07	5.18	4.84	4.84	4
Ursa Minor Dwarf dE4	${105.00}_{-0.06}^{+0.62}$, ${44.74}_{-0.06}^{+0.36}$, ${68.41}_{-0.51}^{+0.51}$	${0.16}_{-0.03}^{+0.86}$, ${0.14}_{-0.02}^{+1.45}$, ${2.17}_{-0.59}^{+3.10}$	0.22	0.33	4.35	19.77	13.11	53

Note. The best-fit positions (l, b, D) and extent (σ_l, σ_b, σ_D) of dwarf galaxies from Table 1, along with their 1σ uncertainties. Assuming an ellipsoidal shape for each dwarf galaxy, we calculate their axis ratios by first translating their angular extent (σ_l, σ_b) into a linear extent (Δl, Δb) as given by Equations (9) and (10), and then use the line-of-sight depth ΔD = 2σ_D (11) to calculate the axis ratios ΔD/Δl, ΔD/Δb. In this table, Sagittarius Dwarf dSph and Crater II dSph from Table 1 are missing, as we were not able to determine reasonable fits for them. For details on this, see Section 4.

Download table as:  ASCIITypeset image

Table 4.  Fitted Globular Clusters

Name	Fitted	Fitted	Δl [kpc]	Δb [kpc]	ΔD [kpc]	ΔD/Δl	ΔD/Δb	Sources
	(l [°], b [°], D [kpc])	(σl [°], σb [°], σD [kpc])
NGC 2419	${180.36}_{-0.03}^{+0.03}$, ${25.24}_{-0.03}^{+0.04},{79.70}_{-0.37}^{+0.32}$	${0.11}_{-0.01}^{+0.01}$, ${0.11}_{-0.01}^{+0.02}$, ${4.24}_{-1.14}^{+1.33}$	0.28	0.30	8.47	30.25	27.81	8
NGC 4590 (M68)	${299.62}_{-0.08}^{+0.12}$, ${36.07}_{-0.11}^{+0.10}$, ${10.48}_{-0.28}^{+0.26}$	${0.15}_{-0.04}^{+0.68}$, ${0.15}_{-0.04}^{+0.65}$, ${0.66}_{-0.13}^{+1.29}$	0.04	0.05	1.32	33.0	24.15	5
NGC 5024 (M53)	${332.93}_{-0.12}^{+0.12}$, ${79.74}_{-0.04}^{+0.04}$, ${18.25}_{-0.14}^{+0.13}$	${0.35}_{-0.08}^{+0.12}$, ${0.11}_{-0.01}^{+0.02}$, ${0.55}_{-0.03}^{+0.08}$	0.04	0.07	1.09	15.57	15.31	12
NGC 5053	${335.78}_{-0.18}^{+0.19}$, ${78.93}_{-0.14}^{+0.16}$, ${16.66}_{-0.26}^{+0.28}$	${0.30}_{-0.16}^{+1.08}$, ${0.18}_{-0.06}^{+1.10}$, ${0.75}_{-0.20}^{+3.69}$	0.03	0.10	1.50	50.0	14.54	4
NGC 5272 (M3)	${42.20}_{-0.07}^{+0.08}$, ${78.71}_{-0.02}^{+0.02}$, ${10.48}_{-0.07}^{+0.07}$	${0.45}_{-0.05}^{+0.05}$, ${0.10}_{-0.002}^{+0.01}$, ${0.51}_{-0.01}^{+0.02}$	0.03	0.04	1.02	34.0	27.05	56
NGC 5466	${42.13}_{-0.04}^{+0.04}$, ${73.59}_{-0.03}^{+0.04}$, ${15.76}_{-0.14}^{+0.14}$	${0.12}_{-0.02}^{+0.03}$, ${0.11}_{-0.01}^{+0.02}$, ${0.54}_{-0.03}^{+0.07}$	0.02	0.06	1.08	54.0	17.76	10
NGC 5904 (M5)	${3.88}_{-0.04}^{+0.03}$, ${46.77}_{-0.02}^{+0.03}$, ${7.87}_{-0.19}^{+0.19}$	${0.13}_{-0.02}^{+0.04}$, ${0.11}_{-0.005}^{+0.02}$, ${0.53}_{-0.02}^{+0.08}$	0.02	0.03	1.05	52.5	36.01	24
NGC 6229	${73.64}_{-0.04}^{+0.04}$, ${40.31}_{-0.04}^{+0.04}$, ${29.94}_{-0.19}^{+0.17}$	${0.11}_{-0.01}^{+0.02}$, ${0.11}_{-0.01}^{+0.03}$, ${0.61}_{-0.08}^{+0.19}$	0.09	0.12	1.22	13.5	10.31	12
NGC 6864 (M75)	${20.28}_{-0.23}^{+0.25}$, $-{25.76}_{-0.28}^{+0.20}$, ${20.79}_{-0.35}^{+0.32}$	${0.25}_{-0.13}^{+1.46}$, ${0.34}_{-0.21}^{+2.70}$, ${1.59}_{-0.93}^{+4.27}$	0.16	0.24	3.17	19.8	13.01	4
NGC 6934	${52.12}_{-0.04}^{+0.04}$, $-{18.87}_{0.04}^{+0.03}$, ${16.77}_{-0.21}^{+0.21}$	${0.11}_{-0.01}^{+0.03}$, ${0.11}_{-0.01}^{+0.02}$, ${0.57}_{-0.05}^{+0.16}$	0.06	0.07	1.14	19.00	17.14	10
NGC 6981 (M72)	${335.16}_{-0.03}^{+0.03}$, $-{32.70}_{-0.03}^{+0.03}$, ${17.51}_{-0.17}^{+0.15}$	${0.11}_{-0.01}^{+0.01}$, ${0.11}_{-0.01}^{+0.01}$, ${0.56}_{-0.05}^{+0.11}$	0.06	0.07	1.12	18.70	16.90	15
NGC 7006	${63.78}_{-0.03}^{+0.03}$, $-{19.39}_{-0.03}^{+0.03}$, ${40.12}_{-0.15}^{+0.16}$	${0.11}_{-0.004}^{+0.01}$, ${0.11}_{-0.01}^{+0.01}$, ${0.59}_{-0.06}^{+0.11}$	0.15	0.15	1.17	7.80	7.87	16
NGC 7078 (M15)	${65.03}_{-0.08}^{+0.11}$, $-{27.32}_{-0.08}^{+0.07}$, ${11.07}_{-0.22}^{+0.24}$	${0.15}_{-0.04}^{+1.07}$, ${0.13}_{-0.03}^{+0.95}$, ${0.60}_{-0.08}^{+2.69}$	0.05	0.05	1.21	24.20	23.42	10
NGC 7089 (M2)	${53.46}_{0.25}^{+0.22}$, $-{35.81}_{-0.29}^{+0.29}$, ${12.11}_{-0.28}^{+0.39}$	${0.35}_{-0.21}^{+2.38}$, ${0.62}_{-0.47}^{+3.60}$, ${1.47}_{-0.84}^{+6.28}$	0.12	0.26	2.95	24.58	11.24	4
Pal 3	${240.14}_{-0.09}^{+0.10}$, ${41.95}_{-0.18}^{+0.21}$, ${85.05}_{-0.34}^{+0.32}$	${0.14}_{-0.03}^{+0.17}$, ${0.34}_{-0.17}^{+0.31}$, ${1.76}_{-1.08}^{+1.77}$	0.31	1.01	3.53	11.39	3.50	3
Pal 5	${0.87}_{-0.27}^{+0.29}$, ${45.80}_{-0.28}^{+0.26}$, ${21.66}_{-0.30}^{+0.33}$	${0.58}_{-0.43}^{+2.82}$, ${0.31}_{-0.19}^{+2.37}$, ${1.61}_{-0.98}^{+7.52}$	0.31	0.24	3.23	10.41	13.56	3

Note. The best-fit positions (l, b, D) and extent (σ_l, σ_b, σ_D) of globular clusters from Table 2, along with their 1σ uncertainties. Assuming an ellipsoidal shape for each globular cluster, we calculate their axis ratios by first translating their angular extent (σ_l, σ_b) into a linear extent (Δl, Δb) as given by Equations (9) and (10), and then use the line-of-sight depth ΔD = 2σ_D (11) to calculate the axis ratios ΔD/Δl, ΔD/Δb. In this table, NGC 4147, NGC 5634, NGC 5694, NGC 5897, IC 1257, NGC 6093 (M80), NGC 6171 (M107), NGC 6284, NGC 6356, NGC 6402 (M14), NGC 6426, NGC 7099 (M30), Pal 1, and Pal 13 from Table 2 are missing, as we were not able to determine reasonable fits for them. For details on this, see Section 4.

Download table as:  ASCIITypeset image

We also give the axis ratios ΔD/Δl and ΔD/Δb describing the morphology, as well as the number of sources found in the dSph or globular cluster in each case.

5.1. Comments on Individual Dwarf Galaxies and Globular Clusters

5.2. Uncertainty-corrected Depth of Dwarf Galaxies and Globular Clusters

5.3. The Radii of Globular Clusters and Dwarf Galaxies

For those dwarf galaxies and globular clusters from Tables 1 and 2, which do not have enough sources to carry out the fitting process described in Section 4, we derived their mean distances (in the case of finding multiple RRab stars likely associated with the overdensity) or give the distance to the single RRab star found within this overdensity.

Tables 5 and 6 list the distances, along with the number of RRab stars found in each case.

Table 5.  Dwarf Galaxies with Too Few RRab Stars

Name	Mean	Sources	Comment
	$\bar{D}$ [kpc]
Aquarius II dSph	107.87	1
Bootes I dSph	60.61	2
Crater II dSph	105.48	2
Segue 1 dSph	23.24	1	up to two additional sources nearby
Segue 2 dSph	33.31	1
Ursa Major II Dwarf	33.02	1

Note. The mean positions (l, b, D) of those dwarf galaxies from Table 1 that do not have enough sources in the PS1 catalog of RR Lyrae stars for carrying out the fitting process described in Section 4.

Download table as:  ASCIITypeset image

Table 6.  Globular Clusters with Too Few RRab Stars

Name	Mean	Sources	Comment
	$\bar{D}$ [kpc]
IC 1257	27.24	1
NGC 4147	18.54	1
NGC 5634	25.81	1
NGC 5694	33.96	1
NGC 5897	12.91	1	up to three additional sources nearby
NGC 6093	10.74	2
NGC 6171 (M107)	6.01	7
NGC 6356	11.02	1
NGC 6402 (M14)			many field stars at this distance
NGC 6426	19.83	5
NGC 7099 (M30)	8.41	2
Pal 1			nothing detected at this position: mean D = 10.08 kpc
Pal 13	23.59	3

Note. The mean positions (l, b, D) of those globular clusters from Table 2 that do not have enough sources in the PS1 catalog of RR Lyrae stars for carrying out the fitting process described in Section 4.

Download table as:  ASCIITypeset image

In total, for each of the 13 GC and 6 dSph we found at least one RRab star associated with the overdensity. For those with at least two RRab stars, we give the mean distance, and otherwise, the distance from the only RRab star found. In most cases, our distance estimate lies well within the 3% uncertainty we claim for the PS1 3π sample of RR Lyrae stars.

For some overdensities, we find a lot of stars in the field at about the same distance. This is the case for NGC 5897, where one RRab star is very close to the assumed coordinates of this GC, but there are in total up to four stars that could be associated with that GC. For NGC 6402 (M14), the field is even more crowded; there are many sources in the field at that distance without revealing an overdensity.

In the case of NGC 6356, we find one source close to the coordinates given for this GC, but at a different distance: the RRab star from our catalog is at a heliocentric distance of 11.02 kpc, whereas Harris (1996) gives a heliocentric distance of 15.1 kpc for NGC 6356. In the case of Pal 1, we find no RRab stars clearly associated with this GC. For Pal 13, we find three RRab stars for which we calculate a mean distance of 23.59 kpc, which is about 2.5 kpc lower than the distance given by the recent compilation of Harris (1996). Siegel et al. (2010) claim a distance of 24.8 kpc, which is within our distance precision. The same is the case for the dwarf galaxy Bootes I dSph. We find a mean heliocentric distance of 60.61 kpc, which is about 5 kpc off from the distance given by Okamoto et al. (2012). However, our distance estimate matches very well the distance of 60.4 kpc by Hammer et al. (2018). For Segue 1 dSph, it is difficult to identify which sources are likely associated with this dwarf galaxy, as there are many sources in the field at about that distance. For the farthest dwarf galaxy in our sample, Crater II dSph, our heliocentric distance estimate of 105.48 kpc is somewhat lower than distance estimates in the literature, i.e., the 112 kpc claimed by Joo et al. (2018).

In one of our previous papers (Sesar et al. 2017), we used the period–absolute magnitude–metallicity (PLZ) relation known for RR Lyrae stars to calculate the RRab star's distances we use in the paper at hand. The PLZ relation is given as (e.g., Catelan et al. 2004; Sollima et al. 2006):

$$\begin{eqnarray}\begin{array}{rcl}{M}_{\lambda } & = & {\alpha }_{\lambda }{\mathrm{log}}_{10}(P/{P}_{\mathrm{ref}})+{\beta }_{\lambda }({[\mathrm{Fe}/{\rm{H}}]-[\mathrm{Fe}/{\rm{H}}]}_{\mathrm{ref}})\\ & & +\ {M}_{\mathrm{ref},\lambda }+\epsilon ,\end{array}\end{eqnarray} \tag{ 12 }$$

where λ denotes the bandpass, P is the period of pulsation, M_ref is the absolute magnitude at some reference period and metallicity (here chosen to be P_ref = 0.6 days, [Fe/H]_ref = −1.5 dex), and α, β describe the dependence of the absolute magnitude on period and metallicity. The is a standard normal random variable centered on 0 and with a standard deviation of the uncertainty in M_λ in order to model the intrinsic scatter in the absolute magnitude convolved with unaccounted measurement uncertainties.

As PS1 3π itself has no metallicity information available, we constrained the PLZ relation Equation (12) in PS1 bandpasses using metallicities and distance moduli of PS1 RRab stars in the five Galactic globular clusters NGC 6171, NGC 5904, NGC 4590, NGC 6341, and NGC 7078 (Sesar et al. 2017). Table 1 in Sesar et al. (2017) gives the fitted PLZ relations in all bandpasses. The resulting relation in the i_P1 band is then used to constrain distances also for stars where no metallicity is available.

In the case of no available metallicity, the expression for the absolute magnitude in the i_P1 band, ${M}_{{i}_{{\rm{P}}1}}$, simplifies to (Sesar et al. 2017, Equation (5)): ${M}_{{i}_{{\rm{P}}1}}=-1.77{\mathrm{log}}_{10}(P/0.6)+0.46$, and, in general, the expression for the absolute magnitude in the λ_P1 band simplifies to

$$\begin{eqnarray}&&{M}_{{\lambda }_{{\rm{P}}1}}={\alpha }_{\lambda }{\mathrm{log}}_{10}(P/0.6)+{M}_{\mathrm{ref},\lambda }.\end{eqnarray} \tag{ 13 }$$

Distances are then constrained using the dereddened flux-averaged i_P1-band magnitude (this is i_F in Sesar et al. 2017) and Equation (13). This equation was used to calculate the PS1 3π RRab distances we use in this paper.

Now, after having fitted the spatial extent and distance of 16 globular clusters, we are interested in comparing the fitted PLZ relation from Sesar et al. (2017) to fits carried out for each cluster using the [Fe/H] from spectra of red giants of Carretta et al. (2009; Table A1). For each RRab star in each GC, we have the period from the RRab catalog, the [Fe/H]—assumed to be constant for a given GC—from Carretta et al. (2009) and the fitted distance modulus (DM) and distance from the RRab catalog.

For Figure 15, we selected the RRab stars for each globular cluster and plot their dereddended apparent r-band magnitude (r_F in the PS1 RRab catalog) versus their period. The typical trend of a PL relation is clearly visible.

We then took a closer look at the individual globular clusters. For each of them, in each bandpass λ ∈ {g_P1, ..., z_P1}, we plot each star's dereddened apparent magnitude m_λ versus P. We also plot the apparent (unreddened) magnitude as expected from the PLZ relation α_λ log₁₀(P/P_ref) + β_λ([Fe/H] − [Fe/H]_ref) + M_ref + DM versus P, as well as the apparent magnitude as expected from the equation without metallicity α_λ log₁₀(P/P_ref) + M_ref + DM versus P.

This results in Figures 16–31. The error bars in the predicted apparent magnitudes correspond to an uncertainty of ∼0.06 mag in the absolute magnitude and thus DM (Sesar et al. 2017). As the DM was derived from the i_P1 band, in this band, per definition, the observed magnitude and the apparent magnitude as predicted without [Fe/H] are the same. We find that for most of the 16 globular clusters we have evaluated, the predicted apparent magnitude with [Fe/H] (blue markers in the figures) is a bit brighter than the predicted apparent magnitude without taking into account [Fe/H] (black markers), and this is again a bit brighter than the observed dereddened apparent magnitude (orange markers). NGC 6864 (Figure 24) is the only GC where the predicted apparent magnitude with [Fe/H] is higher than the one predicted without [Fe/H]. It has the highest metallicity in the sample of GC studied here.

The offset in the predicted apparent magnitude depends on the metallicity of the GC in this case. The predicted apparent magnitudes with [Fe/H] (blue markers in the figures) are calculated using Equation (12) and the DM for each RRab star given in the PS1 RRab catalog (Sesar et al. 2017). For the black markers, we neglect the term β_λ([Fe/H] − [Fe/H]_ref) from Equation (12), and again use the DM. As β_λ ranges from 0.06 to 0.09, [Fe/H]_ref = −1.5, and [Fe/H], which ranges from −2.33 to −1.29, is <−1.5 for most GC, this term is negative. Thus, for most of the 16 globular clusters we have evaluated, the predicted apparent magnitude with [Fe/H] (blue markers in the figures) is a bit brighter than the predicted apparent magnitude without taking into account [Fe/H] (black markers).

The offset between observed and predicted apparent magnitudes can be explained by the way the distance to the RRab stars was derived. The DM we use here to calculate the predicted magnitudes was derived in Sesar et al. (2017) using the flux-averaged i_P1-band magnitude. Thus, for the i band, the observed magnitude (orange markers) and the magnitude predicted without [Fe/H] agree, while for the other bands, we find the predicted magnitudes to deviate slightly from the observed ones (black versus orange markers). This deviation is on the order of the uncertainty claimed for the DM, 0.06(rnd) ± 0.03 (sys) mag (Sesar et al. 2017).

In this section, we compare the PS1 3π distances to those published for the second Gaia data release (hereafter Gaia DR2; Gaia Collaboration 2018).

According to Bailer-Jones et al. (2018), for the vast majority of stars in Gaia DR2, reliable distances cannot be obtained by inverting the parallax, but should be derived by an algorithm that accounts for the nonlinearity of the transformation. Carrying out a probabilistic approach, Bailer-Jones et al. (2018) published distances to 1.33 billion stars in Gaia DR2.

To compare our heliocentric distance estimates D_PS1 from Sesar et al. (2017) to those of Gaia DR2 Bailer-Jones et al. (2018), we cross-matched our PS1 RRab sample of 44,403 stars with Gaia DR2, and found a cross-match for 43,791 sources. In Figure 32, we show the D_GaiaDR2 and a rough distance estimate 1/parallax versus D_PS1 for the RRab stars within D_PS1 < 20 kpc.

At the present time, we find a rather large scatter in the distances, much larger than the PS1 distance uncertainty of 3% or an estimate of the distance uncertainty from the parallax error. When the parallax error exceeds 10%, which happens at a heliocentric distance of about 5 kpc, the distances from Gaia DR2 become very unreliable. Bailer-Jones et al. (2018) already claim quite large uncertainties of their distance estimates. In Figure 33, we plot the upper and lower 68% confidence interval boundaries of their distance estimates for our cross-matched sample of RRab stars. According to Bailer-Jones et al. (2018), the confidence intervals are asymmetric with respect to the distance estimate D_GaiaDR2 as a consequence of the nonlinear transformation from parallax to distance.

Up to now, the precision of those distances—which are calculated only from geometric principles without any assumptions on astrophysics such as pulsation or PLZ relationships—is not competitive with the precision of our distances from Sesar et al. (2017), and especially cannot be used for the distant GC and dwarfs. However, this might change at least partially for the end-of-mission data. Until then, we strongly recommend using the RRab distances from Sesar et al. (2017) and subsequent analysis instead of those from Gaia DR2.

We started our analysis based on a list of dwarf galaxies within 3 Mpc by McConnachie (2012) and a list of currently known globular clusters from a current online version of the Harris (1996) database. We excluded those outside the PS1 3π footprint and attempted to fit the (l, b, D) distribution of the remaining ones. For the ones for which a fit was not possible due to only a small number of RRab stars available, we instead selected those stars and give their mean distance.

\In Tables 9 and 10, we compare our distances for dwarf galaxies and GC to literature distances. For almost all dwarf galaxies and globular clusters, the estimated distances compared to those in the recent literature are well within our distance precision of 3%. However, there are a few dwarf galaxies and globular clusters for which our distances deviate significantly from those given in the literature.

Table 9.  Distance Comparison for Dwarf Galaxies

Name	D [kpc]	Method	Literature D [kpc]	Method and Reference
Aquarius II dSph	107.87	1 RRab	107.900 ± 3.300	BHB stars (Torrealba et al. 2016b)
Bootes I dSph	60.61	mean of 2 RRab	65.3	(BHB + RR Lyr) HSC/Subaru imaging (Okamoto et al. 2012)
			62 ± 4	15 RR Lyr (Siegel 2006)
			60.4	(Hammer et al. 2018)
Crater II dSph	105.48	mean of 2 RRab	∼120	CMD (Torrealba et al. 2016a)
			112 ± 5	RR Lyr (Joo et al. 2018)
			117.5 ± 5	(McConnachie 2012)
Draco dSph	${74.26}_{-0.18}^{+0.18}$	fit	71 ± 7	SDSS photometry (Odenkirchen et al. 2001)
			75.8 ± 5.4	94 RR Lyr (Bonanos et al. 2004)
Sagittarius dSph	${28.18}_{-0.10}^{+0.10}$	fit	26.3 ± 1.8	RGB tip (Monaco et al. 2004)
Segue 1 dSph	23.24	1 RRab	23 ± 2	CMD fitting, esp. horizontal branch (Belokurov et al. 2007)
Segue 2 dSph	33.31	1 RRab	35	from 4 BHB stars (Belokurov et al. 2009)
Sextans dSph	${81.42}_{-0.40}^{+0.41}$	fit	84.2 ± 3.3	RR Lyr from Dark Energy Camera imaging (Medina et al. 2018)
Ursa Minor Dwarf dE4	${68.41}_{-0.51}^{+0.51}$	fit	76	RR Lyr and HB (Bellazzini et al. 2002)
			76 ± 4	distance from HB, considering metallicity of UMi (Carrera et al. 2002)
Ursa Major I dSph	${94.33}_{-4.94}^{+10.80}$	fit	96.8 ± 4	V mag of HB, HSC/Subaru imaging study (Okamoto et al. 2008)
			${97.3}_{-5.7}^{+6.0}$	variable stars in UMa 1 (Garofalo et al. 2013)
Ursa Major II Dwarf	33.02	1 RRab	${34.7}_{-1.9}^{+2.0}$	1 RR Lyr (Dall'Ora et al. 2012)

Note. Comparison of our distance estimates (column D [kpc]) to reference values from literature. For our distance estimates, we note whether they are a result of the fitting process or are determined as a mean distance from a small number of RRab stars. For literature values, we give the method used to obtain the distance and the reference.

Download table as:  ASCIITypeset image

Table 10.  Distance Comparison for Globular Cluster

Name	D [kpc]	Method	Literature D [kpc]
IC 1257	27.24	1 RRab	25
NGC 2419	${79.70}_{-0.37}^{+0.32}$	fit	82.6
NGC 4147	18.54	1 RRab	19.3
NGC 4590 (M68)	${10.48}_{-0.28}^{+0.26}$	fit	10.3
NGC 5024 (M53)	${18.25}_{-0.14}^{+0.13}$	fit	17.9
NGC 5053	${16.66}_{-0.26}^{+0.28}$	fit	17.4
NGC 5272 (M3)	${10.48}_{-0.07}^{+0.07}$	fit	10.2
NGC 5466	${15.76}_{-0.14}^{+0.14}$	fit	16
NGC 5634	25.81	1 RRab	25.2
NGC 5694	33.96	1 RRab	35
NGC 5897	12.91	1 RRab	12.5
NGC 5904 (M5)	${7.87}_{-0.19}^{+0.19}$	fit	7.5
NGC 6093 (M80)	10.74	2 RRab	10
NGC 6171 (M107)	6.01	7 RRab	5.4
NGC 6229	${29.94}_{-0.19}^{+0.17}$	fit	30.5
NGC 6356	11.02	1 RRab	15.1
NGC 6426	19.83	5 RRab	20.6
NGC 6864 (M75)	${20.79}_{-0.35}^{+0.32}$	fit	20.9
NGC 6934	${16.77}_{-0.21}^{+0.21}$	fit	15.6
NGC 6981 (M72)	${17.51}_{-0.17}^{+0.15}$	fit	17
NGC 7006	${40.12}_{-0.15}^{+0.16}$	fit	41.2
NGC 7078 (M15)	${11.07}_{-0.22}^{+0.24}$	fit	10.4
NGC 7089 (M2)	${12.11}_{-0.28}^{+0.39}$	fit	11.5
NGC 7099 (M30)	8.41	2 RRab	8.1
Pal 3	${85.05}_{-0.34}^{+0.32}$	fit	92.5
Pal 5	${21.66}_{-0.30}^{+0.33}$	fit	23.2
Pal 13	23.59	3 RRab	26

Note. Comparison of our distance estimates (column D [kpc]) to reference values from the literature. For our distance estimates, we note whether they are a result of the fitting process or are determined as a mean distance from a small number of RRab stars. For literature values, we use the 2010 online version of the Harris (1996) catalog.

Download table as:  ASCIITypeset image

In the case of NGC 6356, we find only one source close to the coordinates given for this GC, but at a different distance: while the RRab star from our catalog is at a heliocentric distance of 11.02 kpc, the updated catalog of Harris (1996) gives a heliocentric distance of 15.1 kpc for NGC 6356. For Pal 3, we find three stars within a small distance range, resulting in a heliocentric distance estimate of 85.05 kpc, whereas Harris (1996) gives a distance of 92.5 kpc. For Pal 13, we find three RRab stars resulting in a mean distance of 23.59 kpc, which is about 2.5 kpc off from the distance given by Harris (1996). However, this star might be a member of Pal 13, as Siegel et al. (2010) claim a distance of 24.8 kpc, which is within our distance precision. For IC 1257, we have found only one RRab star associated with this GC and estimated its distance to 27.24 kpc, in comparison to the 25 kpc given by Harris (1996).

For the dwarf galaxy Bootes I dSph, we find a mean heliocentric distance of 60.61 kpc, which is about 5 kpc off from the distance given by Okamoto et al. (2012) and about 1.5 kpc off from the distance given by Siegel (2006). However, our distance estimate matches very well the distance of 60.4 kpc given by Hammer et al. (2018). The most distant dwarf galaxy in our sample is Crater II dSph. Our heliocentric distance estimate of 105.48 kpc for this dwarf galaxy is somewhat off from the 117.5 kpc distance estimate reported by McConnachie (2012), but there are closer distance estimates like the 112 ± 5 kpc claimed by Joo et al. (2018), which agrees within the uncertainties with our result. For Sagittarius dSph, our distance estimate of 28.18 kpc is slightly larger than, but within the uncertainties of the 26.3 ± 1.8 kpc result obtained by Monaco et al. (2004). For Ursa Minor Dwarf dE4, we find a distance of 68.41 kpc, whereas the distance is given as 76 kpc from Bellazzini et al. (2002) as well as Carrera et al. (2002).

In some cases, it is hard to find stars associated with the overdensities, especially if there are many field stars within the assumed distance range of the dwarf galaxy or GC, and there is no apparent overdensity. This is the case for NGC 5897, where one RRab star is very close to the assumed coordinates of this GC, but there are in total up to four stars that could be associated with that GC. For the GC NGC 6402 (M14), the field is even more crowded, so many sources in the field are at its assumed distance without revealing an overdensity. For NGC 6356, we find one source close to the coordinates given for this GC, but at a different distance: the RRab star from our catalog is at a heliocentric distance of 11.02 kpc, whereas Harris (1996) give a heliocentric distance of 15.1 kpc for NGC 6356. In the case of Pal 1, we find no stars clearly associated with this GC. For Segue 1 dSph, it is difficult to identify the sources that might be associated with this dwarf galaxy, as there are many sources in the field at about that distance.

For the GC, even though these sources are closer, in most cases our distance uncertainties are larger than for dwarf galaxies. This probably occurs because we are missing sources near the centers of the GCs as the spatial density of sources is higher than that which can be handled by the PS1 analysis codes.

In this paper we have computed the extents Δl, Δb, ΔD and the axis ratios ΔD/Δl and ΔD/Δl for all dwarf galaxies and GCs in which a sufficient number of RRab were picked up in the PS1 RR Lyr database of Sesar et al. (2017). Our distances to the stellar overdensities we study here, including both GCs and dwarf galaxy satellites of the Milky Way, are accurate to better than 3% when more than eight RRab occur within a system (i.e., a GC or a dSph).

In the past 5 years many groups have attempted to determine distances to some of the dwarf galaxies using RRab, but they have each used their own procedures and calibrations to convert a mean RRab magnitude into a distance (see Tables 9 and 10 for references). Our work is unique in that every object, within the large sample we study, is treated identically and comes from the same survey, including the metallicity dependence of the RR luminosity, so that the distances for our large sample of objects are on the same scale across the entire part of the sky covered by the PS1 3π survey, for all halo stellar overdensities within which a sufficient number of RRab could be detected. Thus overall we believe that our distances for the sample of stellar overdensities in the Milky Way halo, i.e., globular clusters and dwarf galaxies, that we study here are more precise and more homogeneous than those in the published literature.

H.-W.R. acknowledges funding from the European Research Council under the European Unions Seventh Framework Programme (FP 7) ERC grant Agreement No. [321035].

The Pan-STARRS1 Surveys (PS1) have been made possible through contributions of the Institute for Astronomy, the University of Hawaii, the Pan-STARRS Project Office, the Max-Planck Society and its participating institutes, the Max Planck Institute for Astronomy, Heidelberg and the Max Planck Institute for Extraterrestrial Physics, Garching, The Johns Hopkins University, Durham University, the University of Edinburgh, Queen's University Belfast, the Harvard-Smithsonian Center for Astrophysics, the Las Cumbres Observatory Global Telescope Network Incorporated, the National Central University of Taiwan, the Space Telescope Science Institute, the National Aeronautics and Space Administration under grant No. NNX08AR22G issued through the Planetary Science Division of the NASA Science Mission Directorate, the National Science Foundation under grant No. AST-1238877, the University of Maryland, and Eotvos Lorand University (ELTE) and the Los Alamos National Laboratory.

Figures 1–11 give plots of the dwarf spheroidals and globular clusters including their (l, b, D) fit.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Figure 12 give the incompleteness of our RRab sample towards the central regions of globular clusters.

Zoom In Zoom Out Reset image size

Figure 13 gives a fit to two mock overdensities.

Zoom In Zoom Out Reset image size

Figure 14 gives a comparison between the estimated extent of the overdensities in the present and the tidal radii radii from the literature.

Zoom In Zoom Out Reset image size

Figure 15 shows the typical trend of a PL relation we get from dereddened r-band magnitudes and periods of the globular clusters.

Zoom In Zoom Out Reset image size

Figures 16–31 give observed and predicted apparent magnitudes for the globular clusters, and PL relations constructed from that.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Figure 32 compares compare our RRab distance estimates to those of Gaia DR2.

Zoom In Zoom Out Reset image size

Figure 33 shows the confidence interval boundaries on the Gaia distances of RRab stars.

Zoom In Zoom Out Reset image size